In what scenarios, would an Incident lead to a Problem? If an Incident is not resolved, would that lead to a Problem Ticket to be raised? Or is it only when many Incidents are reported about a similar issue?

an incident will become a problem when the root underlying cause is not identified. If an incident is not resolved but the root cause is know then it is still an incident, then you have to escalate it (functional escalation) to higher support staff. If that still doesnt fix the incident, then the issue is with the skills of your staff.

Now if you have one or more incidents with the same issue but the root cause is not identified as i mentioned earlier then it becomes a problem. there is a process for that. So what I would suggest for a start is go do some reading about ITIL. Because its basics and your posting it on the wrong thread.

If an Incident is unresolved you get on with resolving it and worry about whether you have a Problem after the poor users have their service back and can get on with their jobs.

There's tons of stuff on this tucked away in these fora. you should be able to find it easily._________________"Method goes far to prevent trouble in business: for it makes the task easy, hinders confusion, saves abundance of time, and instructs those that have business depending, both what to do and what to hope."
William Penn 1644-1718